Nonlinear dynamic analysis of rotating pipe conveying fluid by the finite element method

The rotating pipe conveying fluid is considered. Non-linear (geometrical non-linearity) equation of the motion of the pipe is derived using the finite element method. The equation of motion is derived based of the following assumptions: fluid is incompressible and inviscid; rotory inertia and shear deformation of the pipe are neglected. The sources of parametric vibration are: fluid velocity and pressure, angular speed of pipe. The possibility to solve a non-linear response problem including sub- and/or super-harmonic using the finite element method is shown. Numerical results are derived considering the rotating contilevered pipe conveying fluid. All matrices and vectors of the finite element method are derived by the symbolic computation system Maple

Dynamic processes in the oil pipelines. Part II. The leak identification by numerical methods

The analysis of identification method of leaks occurring due to damages of the linear part of the main oil pipelines is carried out. The momentum and continuity equations of viscous compressible fluid in a pressure pipeline are presented. Differential equations of fluid movement in the oil pipeline are solved by the method of characteristics. Variation diagrams of pressure and velocity of fluid of a leaking oil pipeline are presented

Dynamic processes in the main oil pipelines. Part I. The analysis of causes of leakage occurrence in oil pipelines and leak identification methods

The causes of accidental damages and the damages in oil pipelines are presented. The analysis of identification methods of leaks occurring due to the damages of the linear part of the main oil pipelines is carried out. The momentum and continuity equations of viscous compressible fluid in a pressure pipeline are presented. Differential equations of fluid movement in the oil pipeline are solved by the method of characteristics. Variation diagrams of pressure and velocity of fluid of a leaking oil pipeline are presented

Vehicle gearbox dynamics: centre distance influence on mesh stiffness and spur gear dynamics

Vehicle gearbox dynamics is characterized by time varying mesh stiffness. The paper presents a survey of methods used for determining mesh stiffness and the analysis of the centre distance influence on it. The refined mathematical transmission model presenting the centre distance as a variable is presented. The centre distance error as well as backlash and bearing flexibility is defined and the influence of these factors on mesh stiffness and spur gear dynamics is investigated. The results obtained from this paper may be used in gear-box diagnostics

Simulation of dynamic processes in hydraulic accumulators

The article focuses on pressure pulsations in hydraulic systems, the means reducing them and examines the structure of hydraulic accumulators, including their features and differences. Using the method of characteristics and Fortran software, a dynamic model of a hydraulic system is created. By changing the content of a hydraulic accumulator, the paper analyzes the amplitude of pressure waves, the distance between hydraulic accumulators and the dependency of the pulsations of pressure waves on the aforementioned sizes

Badanie dynamicznych procesów zachodzących w układzie „pojazd-tor” z wykorzystaniem nowej metody dla kół z metalową łuską

Mathematical models of vehicle wheel with metal scales are introduced in this article. When analysing the interaction between vehicle wheel with a metal scale and rail in the system “Vehicle – Track”, the changes of the kinematic and dynamic parameters of the wheel and rail contact points in time are examined, depending on the height of the 2 mm metal scale, when the length of the metal scale is 100 mm and the speed of movement is V = 40 - 100 km/h. The results obtained after the research of the system “Vehicle – Track”, when the wheel has a metal scale, help to better understand and evaluate the impact of metal scale on wheel on dynamic loads of rail and vehicle and the regularities of their movement. The appearance of a metal scale on the wheel’s surface causes technical and maintenances problems for the rolling stock. Railway standards limit the speed of movement that depends on a certain size of metal scale.W niniejszym artykule przedstawiono modele matematyczne koła pojazdu szynowego z powstałą w wyniku zużycia metalową łuską. Analizując oddziaływania pomiędzy kołem pojazdu z łuską a szyną w układzie "pojazd–tor", badano zmiany kinematycznych i dynamicznych parametrów punktów kontaktu koła z szyną zachodzące w czasie, w zależności od wysokości metalowej łuski (2mm), przy długości łuski 100 mm i zakresie prędkości ruchu pojazdu V = 40–100 km/h. Wyniki uzyskane w badaniu układu "pojazd–tor" dla kół na powierzchni których powstała metalowa łuska, umożliwiają lepsze zrozumienie oraz ocenę wpływu łuski na dynamiczne obciążenia szyny i pojazdu oraz prawidłowości ruchu pojazdu. Pojawienie się metalowej łuski na powierzchni koła powoduje problemy techniczne i obsługowe w utrzymaniu ruchu taboru kolejowego. Normy kolejowe ograniczają prędkość ruchu pojazdów szynowych, uzależniając ją od rozmiaru łuski

Investigation of hydrodynamic processes of the extinguishing device

The main aim of the investigation is to develop an approach to investigate hydrodynamic processes in the extinguishing device. The mathematical model of the extinguishing device is presented where the flow of fluid and gas and the interaction of liquid with gas are taken into account. The flow of fluid in a hydraulic system is described by a system of equations of a hyperbolic type which is solved by a characteristics method. An instance of the mathematical simulation of the activity extinguishing device is shown. The dependence of recoil force is obtained

Investigation into the stability of driving an automobile on the road pavement with ruts

The article reviews the stability of an automobile on the road pavement with ruts. The problems of road safety depend on many factors. One of those is the quality of the road surface. Big heavy lorries deform the road surface causing ruts especially in the first line of the road. The article analyzes the influence of the geometry of ruts on the stability of the automobile. A mathematical model of a 3D automobile and the interaction between wheels and the road surface and the geometry of the road surface are presented. The mathematical criterion of the stability of the moving automobile on the road surface with ruts is laid down. The results of mathematical simulation and the criterion of the stability of the moving automobile (60 km/h) on the road surface depending on the depth of ruts are introduced